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First hitting time of the integer lattice by symmetric stable processes

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  • Isozaki, Yasuki

Abstract

For one-dimensional Brownian motion, the first hitting time of a point has infinite mean while the exit time from an interval has finite exponential moments. In this note we establish its counterparts for symmetric stable processes. The Laplace transform of the first hitting time of the integer lattice is obtained.

Suggested Citation

  • Isozaki, Yasuki, 2015. "First hitting time of the integer lattice by symmetric stable processes," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 50-53.
    • Handle: RePEc:eee:stapro:v:98:y:2015:i:c:p:50-53
    DOI: 10.1016/j.spl.2014.12.013
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    Cited by:

    1. Isozaki, Yasuki, 2019. "The first hitting time of the integers by symmetric Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 129(5), pages 1782-1794.

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